menuicon

MATH1011 Quizzes

Quiz 2: Sinusoidal functions and proportionality
Question 1 Questions
Which of the following correctly describes the function shown ?
PIC
a)
y = 2cos 4 3(x 3π 8 )
b)
y = 2sin 4 3x
c)
A sinusoidal function with amplitude 2, period 3π 2 and mean level 0.
d)
All of the above.

Choice (a) is incorrect
Choice (b) is incorrect
Choice (c) is incorrect
Choice (d) is correct!
Find the amplitude and the mean level of the function f(x) = 2sin 2π 3 (x 4) + 1.
a)
Amplitude = 1, mean value = 2.
b)
Amplitude = 2, mean value = 1.
c)
Amplitude = 3, mean value = 4.
d)
Amplitude = 4, mean value = 3.

Choice (a) is incorrect
Choice (b) is correct!
Choice (c) is incorrect
Choice (d) is incorrect
Find the period of the function f(x) = 2sin 2π 3 (x 4) + 1.
a)
2π 3
 b)
3 2π
c)
1 3
 d)
3

Choice (a) is incorrect
Choice (b) is incorrect
Choice (c) is incorrect
Choice (d) is correct!
Period = 2π2π 3 = 3.
Find the period and the amplitude of the function f(x) = 4sin(3x 5) + π.
a)
Amplitude = 4, period = 2π.
b)
Amplitude = 5, period = 2π.
c)
Amplitude = 4, period = 2π 3 .
d)
Amplitude = 5, period = 2π 3 .

Choice (a) is incorrect
Choice (b) is incorrect
Choice (c) is correct!
Choice (d) is incorrect
If y = 4sin(3x π) + 5, which of the following is true ?
a)
4 y 4
 b)
1 y 9
c)
1 y 5
 d)
4 y 9

Choice (a) is incorrect
Choice (b) is correct!
Choice (c) is incorrect
Choice (d) is incorrect
Which of the following has period π 2 and amplitude 4 ?
a)
y = 4sin4x
 b)
y = 4cos π 2 x
c)
y = π 2 sin4x
 d)
y = 4cos4x

Choice (a) is correct!
Note that 4 is also correct.
Choice (b) is incorrect
Choice (c) is incorrect
Choice (d) is correct!
Note that 1 is also correct.
Which of the following has period 2 and amplitude 3 ?
a)
y = 2sin3x
 b)
y = 3cos2x
c)
y = 2sinπx
 d)
y = 3cosπx

Choice (a) is incorrect
1 has amplitude 2, period 2π 3 .
Choice (b) is incorrect
2 has amplitude 3, period π.
Choice (c) is incorrect
3 has amplitude 2, period 2.
Choice (d) is correct!
Which of the following has period 4π and amplitude 1 2 and is such that f(0) = 1 2 ?
a)
y = 1 2sin4x
 b)
y = 1 2cos 1 2x
c)
y = 1 2sin 1 2x
 d)
y = 1 2cos4x

Choice (a) is incorrect
1 has amplitude 1 2, period π 2 .
Choice (b) is correct!
Choice (c) is incorrect
3 has amplitude 1 2, period 4π, but f(0) = 0.
Choice (d) is incorrect
4 has period 1 2, period π 2 .
Expand sin2(x + π 3 ).
a)
3 2 cos2x + 1 2sin2x
 b)
3 2 cos2x 1 2sin2x
c)
3 2 sin2x + 1 2cos2x
 d)
3 2 sin2x 1 2cos2x

Choice (a) is incorrect
Choice (b) is correct!
sin2(x + π 3 ) = sin(2x + 2π 3 ) = sin2xcos 2π 3 + cos2xsin 2π 3 = 1 2sin2x + 3 2 cos2x
Choice (c) is incorrect
Choice (d) is incorrect
The sinusoidal function f is illustrated below.
PIC
The function g has mean level 0, amplitude half that of f, and period twice that of f. Find the equation for the function g.
a)
g(x) = 3 2cos2x
 b)
g(x) = 3cosπx
c)
g(x) = 3 2cosπx
 d)
g(x) = 3cos2x

Choice (a) is correct!
Since f has period π 2 and amplitude 3, g must have amplitude 3 2 and period π.
Choice (b) is incorrect
Choice (c) is incorrect
Choice (d) is incorrect